Honors Geometry Summer Math Packet
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1 Honors Geometry Summer Math Packet Dear students, The problems in this packet will give you a chance to practice geometry-related skills from Grades 6 and 7. Do your best to complete each problem so that you are ready for a strong start in the fall!
2 GRADE 6 MATHEMATICS BY Unit 1: End-of-Unit Assessment 1. Polyhedron P is a cube with a corner removed and relocated to the top of P. Polyhedron Q is a cube. How do their surface areas compare? A. P s surface area is less than Q s surface area. B. P s surface area is equal to Q s surface area. C. P s surface area is greater than Q s surface area. D. There is not enough information given to compare their surface areas. Unit 1: Area and Surface Area Lesson J: End-of-Unit Assessment 1
3 GRADE 6 MATHEMATICS BY 2. Select all of the nets that can be folded and assembled into a triangular prism like this one. 3. A cube has a side length of 8 inches. Select all the values that represent the cube s volume in cubic inches. A. B. C. D. E. Unit 1: Area and Surface Area Lesson J: End-of-Unit Assessment 2
4 GRADE 6 MATHEMATICS BY 4. a. A square has a side length. What is its area? b. A square has an area of. What is its side length? 5. For each pair of numbers, circle the number that is greater. a. or b. or c. or 6. A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning. Unit 1: Area and Surface Area Lesson J: End-of-Unit Assessment 3
5 GRADE 6 MATHEMATICS BY 7. Here is a net made of right triangles and rectangles. All measurements are given in centimeters. a. If the net were folded and assembled, what type of polyhedron would it make? b. What is the surface area of the polyhedron? Explain your reasoning. Unit 1: Area and Surface Area Lesson J: End-of-Unit Assessment 4
6 Unit 1: End-of-Unit Assessment You will need a centimeter ruler for the problem in which you draw a bedroom floor plan. 1. Quadrilateral is a scaled copy of quadrilateral. Select all of the true statements. A. Segment is twice as long as segment. B. Segment is twice as long as segment. C. The measure of angle is twice the measure of angle. D. The length of segment is 16 units. E. The area of is twice the area of. 2. Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B. A. 4.5 inches by 1.5 inches B. 8 inches by 2 inches C. 10 inches by 4 inches D inches by 4.5 inches E. 90 inches by 30 inches 3. A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area of the actual park, in square yards? A. 35 B. 200 C. 1,400 D. 56,000 Unit 1: Scale Drawings Lesson E: End-of-Unit Assessment 1
7 4. Here is a polygon. Draw a scaled copy of the polygon using a scale factor of. 5. The scale of a map says that 4 cm represents 5 km. a. What distance on the map (in centimeters) represents an actual distance of 4 kilometers? b. What is the actual number of kilometers that is represented by 5 centimeters on the map? 6. There are two different maps of Ohio. The scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati is 40 cm. The scale on the second map is 1 cm to 50 km. What is the distance from Cleveland to Cincinnati on the second map? Explain your reasoning. Unit 1: Scale Drawings Lesson E: End-of-Unit Assessment 2
8 7. Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 5 m and width 3 m. She decides on a scale of 1 to 50. a. Draw and label the dimensions of a scale drawing of Elena s bedroom, using a scale of 1 to 50. b. Elena s bedroom door is 0.8 m wide. How wide should the door be on the scale drawing? Explain how you know. c. Elena s bed measures 4 cm by 3 cm on the scale drawing. What are the actual measurements of her bed? Unit 1: Scale Drawings Lesson E: End-of-Unit Assessment 3
9 Unit 3: End-of-Unit Assessment Consider allowing access to a calculator. 1. A circle has radius 50 cm. Which of these is closest to its area? A. 157 cm B. 314 cm C. 7,854 cm D. 15,708 cm 2. Select all the expressions that correctly calculate the perimeter of the shape. A. B. C. D. E. Unit 3: Measuring Circles Lesson E: End-of-Unit Assessment 1
10 3. Select all of the true statements. A. is the area of a circle of radius 1. B. is the area of a circle of diameter 1. C. is the circumference of a circle of radius 1. D. is the circumference of a circle of diameter 1. E. is the constant of proportionality relating the diameter of a circle to its circumference. F. is the constant of proportionality relating the radius of a circle to its area. 4. A class measured the radius and circumference of various circular objects. The results are plotted on the graph. a. Does there appear to be a proportional relationship between the radius and circumference of a circle? Explain or show your reasoning. b. Why might the measured radii and circumferences not be exactly proportional? Unit 3: Measuring Circles Lesson E: End-of-Unit Assessment 2
11 5. For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning. a. The distance around a circular track. b. The total number of equally-sized tiles on a circular floor. c. The amount of oil it takes to cover the bottom of a frying pan. d. The distance your car will go with one turn of the wheels. Unit 3: Measuring Circles Lesson E: End-of-Unit Assessment 3
12 6. This figure is made from a part of a square and a part of a circle. a. What is the perimeter of this figure, to the nearest unit? b. What is the area of this figure, to the nearest square unit? 7. A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field? Explain or show your reasoning. Unit 3: Measuring Circles Lesson E: End-of-Unit Assessment 4
13 Unit 7: End-of-Unit Assessment You may use a calculator. You will need a protractor to measure angles and a ruler to draw line segments. 1. Select all the conditions for which it is possible to construct a triangle. A. A triangle with angle measures,, and B. A triangle with side lengths 4 cm, 5 cm, and 6 cm C. A triangle with side lengths 4 cm, 5 cm, and 15 cm D. A triangle with side lengths 4 cm and 5 cm and a angle E. A triangle with angle measures and, and a 3 cm side length 2. A square pyramid is sliced parallel to the base and halfway up the pyramid. Which of these describes the cross section? A. A square smaller than the base B. A quadrilateral that is not a square C. A square the same size as the base D. A triangle with a height the same as the pyramid Unit 7: Angles, Triangles, and Prisms Lesson F: End-of-Unit Assessment 1
14 3. Which of these describes a unique polygon? A. A triangle with angles,, and B. A quadrilateral with each side length 5 cm C. A triangle with side lengths 6 cm, 7 cm, and 8 cm D. A triangle with side lengths 4 cm and 5 cm and a angle 4. Here is a triangular prism. a. What is the volume of the prism, in cubic centimeters? b. What is the surface area of the prism, in square centimeters? Unit 7: Angles, Triangles, and Prisms Lesson F: End-of-Unit Assessment 2
15 5. Draw as many different triangles as possible that have two sides of length 4 cm and a angle. Clearly mark the side lengths and angles given. 6. What are the values of and? Unit 7: Angles, Triangles, and Prisms Lesson F: End-of-Unit Assessment 3
16 7. For each statement, provide an example showing that the statement can be true, or an explanation of why the statement can never be true. a. Adjacent angles can be complementary. b. Vertical angles can be supplementary. c. Complementary angles can be supplementary. Unit 7: Angles, Triangles, and Prisms Lesson F: End-of-Unit Assessment 4
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